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9. In the following exercise: i. Identify the function's local extreme values in the given domain, and say where they occur. Which of the extreme values, if any, are absolute? f(x) = 2x - x², -∞0< x≤2 ii. a. i. ii. Local maximum: 1 at x = 1; local minimum: 0 at x = 2 Absolute maximum: 1 at x = 1; no absolute minimum b. g(x)=x² - 4x + 4, 1 ≤ x < ∞o i. ii. Local maximum: 1 at x = 1; local minimum: 0 at x = 2 No absolute maximum: absolute minimum: 0 at x = 2

9. In the following exercise: i. Identify the function's local extreme values in the given domain, and say where they occur. Which of the extreme values, if any, are absolute? f(x) = 2x - x², -∞0< x≤2 ii. a. i. ii. Local maximum: 1 at x = 1; local minimum: 0 at x = 2 Absolute maximum: 1 at x = 1; no absolute minimum b. g(x)=x² - 4x + 4, 1 ≤ x < ∞o i. ii. Local maximum: 1 at x = 1; local minimum: 0 at x = 2 No absolute maximum: absolute minimum: 0 at x = 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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can you alos explain how they came up with the answers in blue writing? thanks . i just need explain step by step to understand .thanks 

9. In the following exercise: i. Identify the function's local extreme values in the given domain, and say where they occur. ii. Which of the extreme values, if any, are absolute? a. f(x) = 2x-x², -∞0 < x≤2 i. ii. Local maximum: 1 at x = 1; local minimum: 0 at x = 2 Absolute maximum: 1 at x = 1; no absolute minimum b. g(x) = x² - 4x+4, 1 ≤ x <∞ 1. 11. CO Local maximum: 1 at x = 1; local minimum: 0 at x = 2 No absolute maximum; absolute minimum: 0 at x = 2
Transcribed Image Text:9. In the following exercise: i. Identify the function's local extreme values in the given domain, and say where they occur. ii. Which of the extreme values, if any, are absolute? a. f(x) = 2x-x², -∞0 < x≤2 i. ii. Local maximum: 1 at x = 1; local minimum: 0 at x = 2 Absolute maximum: 1 at x = 1; no absolute minimum b. g(x) = x² - 4x+4, 1 ≤ x <∞ 1. 11. CO Local maximum: 1 at x = 1; local minimum: 0 at x = 2 No absolute maximum; absolute minimum: 0 at x = 2
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